A Note on the Practicality of Maximal Planar Subgraph Algorithms

Given a graph $G$, the NP-hard Maximum Planar Subgraph problem (MPS) asks for a planar subgraph of $G$ with the maximum number of edges. There are several heuristic, approximative, and exact algorithms to tackle the problem, but---to the best of our knowledge---they have never been compared competitively in practice. We report on an exploratory study on the relative merits of the diverse approaches, focusing on practical runtime, solution quality, and implementation complexity. Surprisingly, a seemingly only theoretically strong approximation forms the building block of the strongest choice.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

The Open Graph Archive: A Community-Driven Effort

In order to evaluate, compare, and tune graph algorithms, experiments on well designed benchmark sets have to be performed. Together with the goal of reproducibility of experimental results, this creates a demand for a public archive to gather and store graph instances. Such an archive would ideally allow annotation of instances or sets of graphs with additional information like graph properties and references to the respective experiments and results. Here we examine the requirements, and introduce a new community project with the aim of producing an easily accessible library of graphs. Through successful community involvement, it is expected that the archive will contain a representative selection of both real-world and generated graph instances, covering significant application areas as well as interesting classes of graphs.Comment: 10 page

Integrative visual analysis of protein sequence mutations

BACKGROUND: An important aspect of studying the relationship between protein sequence, structure and function is the molecular characterization of the effect of protein mutations. To understand the functional impact of amino acid changes, the multiple biological properties of protein residues have to be considered together. RESULTS: Here, we present a novel visual approach for analyzing residue mutations. It combines different biological visualizations and integrates them with molecular data derived from external resources. To show various aspects of the biological information on different scales, our approach includes one-dimensional sequence views, three-dimensional protein structure views and two-dimensional views of residue interaction networks as well as aggregated views. The views are linked tightly and synchronized to reduce the cognitive load of the user when switching between them. In particular, the protein mutations are mapped onto the views together with further functional and structural information. We also assess the impact of individual amino acid changes by the detailed analysis and visualization of the involved residue interactions. We demonstrate the effectiveness of our approach and the developed software on the data provided for the BioVis 2013 data contest. CONCLUSIONS: Our visual approach and software greatly facilitate the integrative and interactive analysis of protein mutations based on complementary visualizations. The different data views offered to the user are enriched with information about molecular properties of amino acid residues and further biological knowledge

A New Approach for Visualizing UML Class Diagrams

UML diagrams have become increasingly important in the engineering and reengineering processes for software systems. Of particular interest are UML class diagrams whose purpose is to display class hierarchies (generalizations), associations, aggregations, and compositions in one picture. The combination of hierarchical and non-hierarchical relations poses a special challenge to a graph layout tool. Existing layout tools treat hierarchical and non-hierarchical relations either alike or as separate tasks in a two-phase process as in, e.g., cite{See97}. We suggest a new approach for visualizing UML class diagrams leading to a balanced mixture of the following aesthetic criteria: Crossing minimization, bend minimization, uniform direction within each class hierarchy, no nesting of one class hierarchy within another, orthogonal layout, merging of multiple inheritance edges, and good edge labelling. We have realized our approach within the graph drawing library GoVisual. Experiments show the superiority to state-of-the-art and industrial standard layouts

A New Approach for Visualizing UML Class Diagrams

UML diagrams have become increasingly important in the engineering and reengineering processes for software systems. Of particular interest are UML class diagrams whose purpose is to display class hierarchies (generalizations), associations, aggregations, and compositions in one picture. The combination of hierarchical and non-hierarchical relations poses a special challenge to a graph layout tool. Existing layout tools treat hierarchical and non-hierarchical relations either alike or as separate tasks in a two-phase process as in, e.g., cite{See97}. We suggest a new approach for visualizing UML class diagrams leading to a balanced mixture of the following aesthetic criteria: Crossing minimization, bend minimization, uniform direction within each class hierarchy, no nesting of one class hierarchy within another, orthogonal layout, merging of multiple inheritance edges, and good edge labelling. We have realized our approach within the graph drawing library GoVisual. Experiments show the superiority to state-of-the-art and industrial standard layouts

CelticGraph: Drawing Graphs as Celtic Knots and Links

Celtic knots are an ancient art form often attributed to Celtic cultures, used to decorate monuments and manuscripts, and to symbolise eternity and interconnectedness. This paper describes the framework CelticGraph to draw graphs as Celtic knots and links. The drawing process raises interesting combinatorial concepts in the theory of circuits in planar graphs. Further, CelticGraph uses a novel algorithm to represent edges as B\'ezier curves, aiming to show each link as a smooth curve with limited curvature.Comment: Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023

Role of copper interstitials in CuInSe₂: First-principles calculations

Formation enthalpies and migration barriers of copper interstitials and Frenkel pairs in CuInSe₂ (CIS) are determined by first-principles calculations within density functional theory using the nonlocal screened exchange Heyd-Scuseria-Ernzerhof (HSE06) functional. Interstitials occur on four symmetrically inequivalent sites with formation enthalpies of 0.17–0.38 eV, which are much lower than previously reported values based on local approximations. A direct interstitial and indirect interstitialcy diffusion mechanism with migration barriers as low as 0.22 and 0.34 eV are identified. The results provide evidence that the fast interstitial diffusion of copper is important for understanding metastabilities, Fermi-level pinning at interfaces, electric-field-induced creation of p-n junctions, and widely varying experimentally measured diffusion coefficients in CIS devices

First-principles study of the structure and stability of oxygen defects in zinc oxide

A comparative study on the structure and stability of oxygen defects in ZnO is presented. By means of first-principles calculations based on local density functional theory we investigate the oxygen vacancy and different interstitial configurations of oxygen in various charge states. Our results reveal that dumbbell-like structures are thermodynamically the most stable interstitial configurations for neutral and positive charge states due to the formation of a strongly covalent oxygen–oxygen bond. For negative charge states the system prefers a split-interstitial configuration with two oxygen atoms in almost symmetric positions with respect to the associated perfect lattice site. The calculated defect formation energies imply that interstitial oxygen atoms may provide both donor- and acceptor-like defects